**Q1. Two numbers are such that the sum of twice the first number and thrice the second number is 36 and sum of thrice the first number and twice the second number is 39. Which is the smaller number?**

(a) 9

(b) 5

(c) 7

(d) None of these

**Q2. If the sum and difference of two numbers are 20 and 8 respectively, then the difference of their square is:**

(a) 12

(b) 28

(c) 80

(d) 160

**Q3. A 4-digit number is formed by repeating a 2-digit number such as 2525, 3232, etc. Any number of this form is always exactly divisible by:**

(a) 7

(b) 11

(c) 13

(d) Smallest 3-digit prime number

**Q4. A number divided by 68 gives the quotient 269 and remainder zero. If the same number is divided by 67, then the remainder is:**

(a) 0

(b) 1

(c) 2

(d) 3

**Q5. The sum of the digits of a two-digit number is 81 less than the number. What is the difference between the digits of the number?**

(a) 6

(b) 3

(c) 1

(d) Cannot be determined

**Q6. If the digits of a two-digit number are interchanged, the number so obtained is greater than the original number by 27. If the sum of two digits of the number is 11, what is the original number?**

(a) 47

(b) 38

(c) 74

(d) Cannot be determined

**Q7. If the digit in the units place of a two-digit number is halved and the digit in the tens place is doubled, the number thus obtained is equal to the number obtained by interchanging the digits. Which of the following is definitely true?**

(a) Digits in the units place and the tens place are equal.

(b) Sum of the digits is a two-digit number.

(c) Digit is the units place is half of the digit in the tens place.

(d) Digit in the units place is twice the digit in the tens place.

**Q8. If the two digits of the age of Mr. Manoj are reversed then, the new age so obtained is the age of his wife 1/11**

**of the sum of their ages is equal to the difference between their ages. If Mr. Manoj is elder than his wife then find the difference between their ages?**

(a) Cannot be determined

(b) 10 years

(c) 8 years

(d) 9 years

**Q9. The digit in the units place of a number is equal to the digit in the tens place of half of that number and the digit in the tens place of that number is less than the digit in units place of half of the number by 1. If the sum of the digits of the number is seven, then what is the number?**

(a) 52

(b) 16

(c) 34

(d) Data inadequate

**Q11. If the sum of two numbers be multiplied by each number separately, the products so obtained are 247 and 114. The sum of the numbers is:**

(a) 19

(b) 20

(c) 21

(d) 23

**Q13. The sum of squares of two numbers is 90 and the squares of their difference is 46. The product of the two numbers is:**

(a) 22

(b) 24

(c) 26

(d) 28

**Q14. Two number are such that their difference, their sum and their product are in the ratio of 1:7:24. The product of the numbers is:**

(a) 24

(b) 36

(c) 48

(d) 60

**Q15. The digits indicated by * in 3422213** so that this number is divisible by 99 are:**

(a) 1, 9

(b) 3, 7

(c) 4, 6

(d) 5, 5